Question

In: Statistics and Probability

Here is a sample data set that appears to be approximately bell-shaped (normal). 40.3 38 35.1...

Here is a sample data set that appears to be approximately bell-shaped (normal).

40.3	38	35.1	21.4	22	29.6
31.4	33.3	26	15.6	33.7	48.6
29.4	46.4	37.4	11.4	38	48.6
28.6	21.7	41.8	26	31.8	38.3
32.9	34.7	38.3	44	35.4	46.4
35.9	31.4	23.3	24.9	14.3	35.7
26.9	27.8	44	30	23.2	37
28.2	27.6	44.7	34.2	48.5	25.1
25.1	31.2	16.8	18.8	26.5	35.4

24681012length (cm)101520253035404550Frequency

What is the mean of this data set? (Round to two decimal places)
Mean=Mean=

What is the standard deviation of this data set? (Round to three decimal places)
SD=SD=

What is the minimum of this data set?
minimum =

How many standard deviations from the mean is minimum in this data set? (Answer accurate to 3 decimal places. Hint: It is best to use the unrounded MeanMean and SDSD for this calculation, not the values reported above.)
Number of SDs =

Is the minimum an unusual value in this data set?

Expert Solution

I am using google spreadsheet to analyse the data:

What is the mean of this data set?

mean = 31.900 {using average() function}

What is the standard deviation of this data set?

standard deviation = 9.085 Actual-value = 9.085277329

What is the minimum of this data set?

min = 11.4

How many standard deviations from the mean is minimum in this data set?

To find this, subtract from mean the minimum value and then divide by the standard deviation.

how far the minimum is from the mean in terms of standard deviation :

(31.900 - 11.4) / 9.085277329 = 2.256397824

Ans: 2.256. Therefore, the minimum is 2.256 times the standard deviations away from the mean.

Is the minimum an unusual value in this data set?

Although this value is quite small compared to other values, because of the underlying assumption that the data is approximately normal, there is a 0.12% probability of occurrence of this number. Check this from z-score table.

orchestra answered 2 years ago

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